When Is a Function Differentiable? (VCE SSCE Mathematical Methods): Quizzes

$\lim_{h \to 0} \frac{f(a+h) - f(a)}{h}$ exists

Gradient is $-1$ left, $1$ right of zero

When pieces join smoothly with no corner

It must be continuous at that point

A sharp corner at that point

Cannot divide by zero in $f'(x)$ formula

Differentiable is stronger than continuous

Yes, like $f(x) = x^{\frac{1}{3}}$ at $x = 0$

It approaches infinity as $h \to 0$

Not always true